Adding axes to figures

Question

I need to add axes to a bunch of figures in my document, I'm trying with tikz but maybe there's an easier and more elegant way to do it (looking at you, overpic)? The result I'm trying to achieve is not like this, I need the axes to have the arrows as well.

I got some MWE working, but the axes are vertically misaligned (they should be outside of the picture). I've tryed adding \vspaces but they don't seem to work as I'd like.

Thanks in advance for your help!

MWE:

\documentclass{scrreprt}
\usepackage{subfig}
\usepackage{graphicx}
\usepackage{tikz}
\begin{document}
    \begin{figure}[h!]
        \vspace{-0.6cm}
        \centering
        \subfloat[]{%
            \begin{tikzpicture}
            \draw [->] (0,0) -- (0.5,0) node[right]{\footnotesize\(y\)};
            \draw [->] (0,0) -- (0,0.5) node[above]{\footnotesize\(x\)};
            \end{tikzpicture}
            \hspace{-1cm}
            \includegraphics[width=0.45\textwidth,height=1cm]{example-image-a}}
        \quad
        \subfloat[]{%
            \begin{tikzpicture}
            \draw [->] (0,0) -- (0.5,0) node[right]{\footnotesize\(y\)};
            \draw [->] (0,0) -- (0,0.5) node[above]{\footnotesize\(x\)};
            \end{tikzpicture}
            \hspace{-1cm}
            \includegraphics[width=0.45\textwidth,height=1cm]{example-image-a}}
        \\
        \subfloat[]{%
            \includegraphics[width=0.45\textwidth,height=1cm]{example-image-a}}
            \hspace{-0.9cm}
            \begin{tikzpicture}
            \draw [->] (0,0) -- (-0.5,0) node[left]{\footnotesize\(y\)};
            \draw [->] (0,0) -- (0,0.5) node[above]{\footnotesize\(x\)};
            \end{tikzpicture}
        \quad
        \subfloat[]{%
            \includegraphics[width=0.45\textwidth,height=1cm]{example-image-a}
            \hspace{-0.9cm}
            \begin{tikzpicture}
            \draw [->] (0,0) -- (-0.5,0) node[left]{\footnotesize\(y\)};
            \draw [->] (0,0) -- (0,0.5) node[above]{\footnotesize\(x\)};
            \end{tikzpicture}}
        \caption{Foo}
    \end{figure}
\end{document}

EDIT I would like the axes to be something like this:

Answer 1

If you don't want to use the heavy tikz weapons, picture mode is sufficient to draw a few arrows:

\documentclass{scrreprt}
\usepackage{subfig}
\usepackage{graphicx}
%\usepackage{tikz}
\begin{document}
    \begin{figure}[htbp]
        \vspace{-0.6cm}
        \centering
        \subfloat[]{%
            \setlength{\unitlength}{\textwidth}
            \begin{picture}(.45,0.1)
                        \put(0,0){\includegraphics[width=0.45\textwidth,height=1cm]{example-image-a}}
                        \put(.46,-.01){\vector(-1,0){.07}}
                        \put(.46,-.01){\vector(0,1){.05}}
                        \put(.453,.045){x}
                        \put(.373,-.014){y}
            \end{picture}
        }
        \caption{Foo}
    \end{figure}
\end{document}

Second approach with the heavy tikz weapons:

\documentclass{scrreprt}
\usepackage{subfig}
\usepackage{graphicx}
\usepackage{tikz}
\begin{document}
    \begin{figure}[htbp]
        \vspace{-0.6cm}
        \centering
        \subfloat[]{%
            \begin{tikzpicture}
            \node (image) at (0,0) {\includegraphics[width=0.45\textwidth,height=1cm]{example-image-a}};
            \draw [->] (image.south west) -- ++(0.5,0) node[right]{\footnotesize\textit{y}};
            \draw [->] (image.south west) -- ++(0,0.5) node[above]{\footnotesize\textit{x}};
            \end{tikzpicture}
        }
    \end{figure}
\end{document}

Off-topic: I would not use [h!] as floating specifier, this is almost always a guarantee for bad image placement

Answer 2

Maybe like this?

\documentclass{article}
\begin{document}
<<test,echo=F,fig.cap="Axis with background image and more.">>=
library(png)
ima <- readPNG("/usr/local/texlive/2018/texmf-dist/tex/latex/mwe/example-image-a.png")
plot(1:2, type='n', xlab="x", ylab="y",xlim=c(0,10),ylim=c(0,7.5),axes=F)
lim <- par()
u <- par("usr") 
rasterImage(ima, u[1]+.5, u[3]+.5, u[2]-.5, u[4]-.5)
arrows(u[1], u[3], u[2], u[3], code = 2, xpd = TRUE) 
arrows(u[1], u[3], u[1], u[4], code = 2, xpd = TRUE)
lines(c(1, 1.2, 1.35,4.5, 6, 8.3, 9.5), c(.6, 1.3, 0.9,2.7, 0.6, 4.7, 7.0), lwd=5, col="blue")
@
\end{document}

Of course, this need R and knitr to be compiled.

If you need only a little axis:

\documentclass{article}
\begin{document}
<<test,echo=F,fig.cap="Axis with background image and more.">>=
library(png)
ima <- readPNG("/usr/local/texlive/2018/texmf-dist/tex/latex/mwe/example-image-a.png")
plot(1:2, type='n', xlab="", ylab="",xlim=c(0,10),ylim=c(0,7.5),axes=F)
lim <- par()
u <- par("usr") 
rasterImage(ima, u[1]+.5, u[3]+.5, u[2]-.5, u[4]-.5)
arrows(u[1], u[3], u[2]/3, u[3], code = 2, xpd = TRUE) 
arrows(u[1], u[3], u[1], u[4]/3, code = 2, xpd = TRUE)
axis(1, at=u[2]/6, tck=0, labels="x") 
axis(2, at=u[4]/6, tck=0, labels="y") 
lines(c(1, 1.2, 1.35,4.5, 6, 8.3, 9.5), c(.6, 1.3, 0.9,2.7, 0.6, 4.7, 7.0), lwd=5, col="blue")
@
\end{document}